What is taylor 1/((x-1)^2) ?

The answer to taylor 1/((x-1)^2) is 1+2x+3x^2+4x^3+5x^4+\ldots

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taylor 1/((x-1)^2)

taylor

\frac{1}{( x - 1 ) ^{2}}

1 + 2 x + 3 x^{2} + 4 x^{3} + 5 x^{4} + \dots

Solution steps

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d x} ( \frac{1}{( x - 1 ) ^{2}} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{1}{( x - 1 ) ^{2}} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{1}{( x - 1 ) ^{2}} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{2}{1 !} x + \frac{6}{2 !} x^{2} + \frac{24}{3 !} x^{3} + \frac{120}{4 !} x^{4} + \dots

Refine

= 1 + 2 x + 3 x^{2} + 4 x^{3} + 5 x^{4} + \dots

x \to 1 lim (\frac{2 - 1}{x ^{3} - 3})

\frac{x ^{3}}{3 - x ^{2}}

\int_{- 9}^{0} \frac{1}{( x - 9 ) ^{2}} d x

\int e^{1 - 2 x} d x

\int e^{x} 17 + e^{x} d x

What is taylor 1/((x-1)^2) ?
The answer to taylor 1/((x-1)^2) is 1+2x+3x^2+4x^3+5x^4+\ldots